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– airhuffJan 29 '17 at 21:15

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$\begingroup$Searching a prominent online store for "lead test kits" I found products for a little as $12 US that test drinking water for lead, nitrites/nitrates and more. This would be a semi-quantitative solution. Your question doesn't state what your specific goals and requirements are; is something like this what you are looking for?$\endgroup$
– airhuffJan 29 '17 at 22:44

3 Answers
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Since this is a science fair experiment, you will need only common chemicals to test the contaminants in water.

Lead

You can use hydrogen sulfide, $\ce{H2S}$ to test lead. (Warning: it has rotten egg smell.) It is a common reagent and can be found in laboratory. You can also use sodium sulfide instead but it too has rotten egg smell.

$$\ce{Pb^2+ + H2S -> PbS + 2H+}$$

Due to the insolubility of lead sulfide in water ($\ce{4.9 \times 10^{-11}g l^{-1}}$), hydrogen sulfide test is such a sensitive test for the detection of lead and also can be detected in filtrate from separation of sparingly soluble lead chloride and other salts and hydrochloric acid.

Nitrate

You can perform the brown ring test because this test is very sensitive to nitrates in solution. You need conc. sulfuric acid and ferrous sulfate. A brown ring is formed at the junction of two layers probably due to formation of $\ce{[Fe(NO)^2+]}$.

Other very specific and expensive test used to detect contaminants are Gallocyanin test and diphenylthiocarbazone test for lead, diphenylamine test and nitron test for nitrate and sulfanilic test and indole test for nitrite but I won't elaborate them since it is a science project. :)

If your son has to perform this experiment in the science fair, I'm sorry to disappoint you but it will not be possible (only if his school has adequate instrumentation such as an Atomic Absorption Spectrophotometer or a Mass Chromatograph. Contamination of water by lead is in the order of parts per billion (1 part of lead per 1 billion parts of water), and although it is sometimes enough to cause health problems, it is indeed a very low amount of lead to be detected by simple experiments such as the reaction with potassium iodide. And I wouldn't recommend leaving a teenager with a big amount of lead in hands because of its extreme toxicity.

To test for nitrates, the brown ring experiment cited by Diego Zamora can possibly provide a visual result in water, since the nitrate concentration in it is not that small. However, test it before with your son so he don't get frustrated if the experiment goes wrong during the fair. Concentrated sulphuric acid can be found as car battery liquid in some specialized stores (is not very difficult to find). Ferrous sulphate can be found in pool products stores. Handle it with extreme care since sulphuric acid is corrosive and a powerful dehydrating compound that can cause severe burns if in contact with skin.

If you're looking for characteristic reations, two come to mind (unfortunately I do not know what chemicals you have access to).

Nitrates can be tested for with the "brown ring test", sulfuric acid and iron(II) sulfate (see here).

For lead you can test with the "golden rain" reaction using any iodine salt that is soluble in water (see here, they're using lead(II) nitrate in this example).

Depending on what else is in your water solution, you might need to divide it into several solutions of ions from the 3 distinct analytical groups that are generally discussed in literature. You can do this using distinct group reagents for each of the groups. If that's what you're looking for, I suggest reading up on it on the internet, it's a big topic but there's plenty of resources covering it quite well.